Algebraic exponentiation for categories of Lie algebras
A category is locally Cartesian closed if, and only if, every pullback functor between slice categories has a right adjoint. Any such pullback functor lifts to the corresponding category of points (the category of split epimorphisms with fixed codomain), and the existence of a right adjoint for the pullback functor implies that its lifting also admits a right adjoint. The category of Lie algebras over a commutative ring \(D\) with a unit is not locally Cartesian closed, and the author considers thus the problem of the existence of a right adjoint to the pullback functor between categories of points of Lie algebras over \(D\). The category of points over such a Lie algebra may be identified with a category of \(D\)-modules which are also modules over the Lie algebra (with compatibility).NEWLINENEWLINE The author proves that the obvious forgetful functor from this category of modules and that of Lie algebras over \(D\) admits a right adjoint which is even explicitly constructed. From that result he deduces the existence of a right adjoint to every pullback functors between categories of points of Lie algebras over \(D\).
scientific article; zbMATH DE number 6094157